The title above this Psalm says, "For the director of music. A Psalm of David", It is almost identical to the last one and conveys the same information. David knew it was a Psalm (inspired by God to teach us things) and it was designed to be sung.
In the previous chapter, David thought about the fact that God knew everything about his life and in effect he wanted to draw upon that knowledge in order to get even closer to God in terms of what God desired for his life. Therefore, this Psalm should be read in context of the last one: If David realizes that God knows all things about his life, then David wants to draw on that knowledge to help him deal with his problems.
When you read about David's life in 1st and 2nd Samuel, you get the impression he was constantly in trouble. He spent years on the run as a fugitive from King Saul. Even when David became a king himself, I'm sure he had to deal with enemies who wanted to overthrow him as the king. Later, one of David's own sons (not Solomon) lead a major rebellion against him, which caused David to flee the country for awhile.
David understood all to well how to deal with violent men who wanted to harm physically as well as verbally. The reference to their "tongues" supports verbal contention or litigation. David constantly cried out to God for help. As children of God, we too have the same privilege of praying to God. To be perfectly forgiven of our sins through Jesus, gives us the privilege of drawing close to Him in the the same way as David. The Lord God wants us to draw near Him for protection from whatever troubles we face.
Do not misunderstand. This does not mean our problems magically go away if we pray about them? They did not for David and I don't think they will go away that quickly for us. However, by making prayer requests like these first three verses, we are effectively saying to God, 'I can't deal with all of this. Dear God, give me the strength and wisdom to deal with the situations that I have to deal with in my life.' I usually find that God, His way and His timing, leads and guides us through the situations that without His help would be impossible for us to overcome on our own.
These three verses end with a "Selah". We have not had to deal with that word in many Psalms. Remember, this is an untranslated word that essentially means to "pause and think about it". David is saying pause for a moment, stop and think about what I just wrote, and hopefully apply to our own lives.